We define a notion of semantic security of multilinear
(a.k.a. graded) encoding schemes, which generalizes a multilinear DDH
assumption: roughly speaking, we require that if two constant-length
sequences (m_0, m_1) are *pointwise statistically indistinguishable*
by algebraic attackers C (obeying the multilinear restrictions) in the
presence of some other elements z, then encodings of these sequences
should be computationally indistinguishable. Assuming the existence of
semantically secure multilinear encodings and the LWE assumption, we
demonstrate the existence of indistinguishability obfuscators for all
polynomial-size circuits.

We rely on the beautiful candidate obfuscation constructions of Garg
et al (FOCS'13), Brakerski and Rothblum (TCC'14) and Barak et al
(EuroCrypt'14) that were proven secure only in idealized generic
multilinear encoding models, and develop new techniques for
demonstrating security in the standard model, based only on semantic
security of multilinear encodings (which trivially holds in the
generic multilinear encoding model).